Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26041571 | C2 | semidirect |
| 3. #26041566 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041556 | C2 | semidirect |
| 6. #26041319 | C2 | semidirect |
| 7. #26041303 | C2 | semidirect |
| 9. C2×C4⋊Q8×C181 | C2 | semidirect |
| 36. #15668449 | Q8 | semidirect |
| 72. Dic362 | C2×Q8 | semidirect |
| 74. D724 | C2×Q8 | semidirect |
| 121. C181 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668449 | 2 |
| #26041571 | 2 |
| #26041566 | 2 |
| #26041561 | 2 |
| #26041556 | 2 |
| #26041319 | 2 |
| #26041303 | 2 |
| #26041278 | 2 |
| C2×C4⋊Q8×C181 | 2 |
| #3079 | 181 |